How to properly texture this cylinder
In the Edit mode delete the top and bottom faces. As we do not need extra faces here.

With the edge selected. Select the top and bottom and any center edge with shift select

With the edge selected press Ctrl+E and select Mark Seam

Now Press A to select all Faces. Press U and select Unwrap

Drag and make a new window -> UV Editor

Click on the new button and navigate the image.

Now in the material tab -> New and select the image from drop down

Note : Before you process the above steps. Press Ctrl+A select Rotation and Scale



Click on the small dot -> image texture



Then click the drop down here (find the same texture you have used in UV editor)